1st Amendment and Free Speech/The federal government restricting freedom of speech in the Newspapers

I am trying to figure out if there is any way one could argue that the Federal Government cannot restrict freedom of speech in the newspapers for this particular situation?

The situation: There's a cave which is one of the deepest caves in the United States, and most citizens in the particular area don't even know it's there, although it's been known for about 60 years. The National Forest Service has a gate on the entrance, because of safety concerns it being a vertical cave that's loose shale, and to protect it from vandalism (although I hear it's supposed to be ugly inside so I don't know who would vandalize).

Anyway, in order to get inside the cave, you need permission and a key from the National Forest Service. One of the things you need to do is sign a contract saying there will be no publicity in the newspaper or Internet because of your trip inside (they don't want the public to get excited about this "gated off cave").

I'm trying to figure out if it's Constitutional for the Federal Government to have people sign away their "Freedom of Speech" like that to go into a natural cave?

Also, let's say someone were to go to the newspapers protesting this, saying people should care because the First Amendment and the Constitution should be important to them. In the second scenario, could the Federal Government take legal action for protesting?

AnswerNick,

The Federal Government certainly retains the right to restrict access to the cave. The confidentiality agreement or non-disclosure agreement required to enter the cave is simply the price you pay to attain permission to pass through. Freedom of Speech (FOS) is generally presumed to be protected, unless a specific exception applies. With that said it is arbitrary as to whether or not signing the agreement is an unlawful restriction on your 1st Amendment protection of (FOS). From your description it appears that the National Forest Service is treating the restriction on FOS using the exception of National Security or some other similar exception to protect Federal property. If the exception falls into a category like National Security then there is no FOS protection. In this case it seems like the restriction would have to be challenged in court for resolution.

The Federal Government could not take action against a person describing what they know to a newspaper if they did not sign the confidentiality/non-disclosure agreement. The Federal Government could impose sanctions on a person who did, but that might be the standing needed to challenge the restriction in court.